H∞ Control of Nonlinear DC Motor Systems: One-Sided Lipschitz Approach *

In this study, we explore the problem of achieving
$H$
∞ control for a specific type of nonlinear systems characterized by one-sided Lipschitz (OSL). Initially, we introduce a model for a nonlinear DC motor. Subsequently, we employ a technique that separates the Lyapunov matrix from the system matrix to establish less conservative conditions for analysis. Following this, we determine the control gain using a decoupling approach technique based on Linear Matrix Inequalities (LMIs), ensuring both asymptotic stability and effective suppression of disturbances in the
$H$
∞ sense. Finally, the proposed approach is validated through simulations demonstrating the controlled behavior of the nonlinear DC motor system.